The Solvability of Fourth-Order Differential Equations under Almost Hardy–Rogers ψ,ϕ-Type Multivalued Contractions in M℘-Metric Space

Abstract

This paper aims to introduce a novel variation of almost Hardy–Rogers ψ,ϕ-type multivalued contraction and ϑ-type contraction mappings. The main focus is on proving new fixed point (FP) results in M℘-metric space (M℘-MS). Additionally, several consequences are derived from our main findings. To elucidate the recency of our outcomes, various examples are provided. Finally, we utilize the obtained results to scrutinize the existence of solutions for nonlinear fourth-order differential equations (NFODEs).